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Your odds of getting into Berkeley or Stanford's EE PhD programs are essentially zero. You might get accepted into Stanford's Master's only program, but even that would be a long shot. I would have recommended applying to some programs in between Berkeley and Stanford and Irvine in terms of prestige, but it's obviously a little late for this application cycle. If you end up reapplying next year though, I would consider this.
In the mean time, if you do want to go to grad school I would certainly try to get some research experience.

To answer both questions: Rains is composed of a number of small buildings. each building is two-three stories tall. There are two numbers relevant for rains, building number (runs from 200-238) and Apartment number. an apartment number of 30x would indicate that you are on the third floor.
Stanford tends to only give you your apartment number after you check in at Stanford, but they might tell you if you ask (they didn't tell me when I asked )

Except $651 is a ridiculously low price to be paying for facilities like Stanford's on-campus housing, so close to campus. It's certainly much cheaper than a lot of the stuff in neighboring Palo Alto. I don't think a private university really needs to justify rate increases for housing--if you don't like it, you can always choose to live off.

If you really want to know, you can look at a Stanford map and find out... but roughly, Lyman is a 5 minute walk from the engineering quad. EV is more like a twenty minute walk / ten minute bike ride or shuttle ride.

You'd probably have to secure an RA (still possible) but if I were you I'd just go to Cornell, where you've got a nice fellowship. That is, unless there is one prof at Stanford you really, really want to work for.

-Munger is brand new, when I was there it was still under construction. I don't know to what extent it's going to be law students, but I am not a law student...
-The floor plans are available online
-That is what I was told. I never visited myself, as I said, it was quite isolated from all the other grad student housing.

I'm guessing this is Zach of Berkeley's EEGSA. Dude, you're awesome! Sorry I didn't end up going to Berkeley, but visit weekend was really fun. I was the guy from Caltech (Florida originally)... the one that didn't eat whole chickens or speak greek.

I lived in Rains for three months while I did an REU at Stanford. Rains is probably the most social housing option, so I would lean toward it for a two-bedroom option. I personally thought Rains was nicer than EV overall and preferred the more social atmosphere. I didn't visit Lyman, mainly because Lyman is way on the other side of the campus from all the other housing. The only reason to live in Lyman is if you're engineering and want somewhere relatively quiet and close to lab.
I'm personally planning to live in Munger. Sure, it's more expensive, but damn, it's nice.